Question

Помогите решить задачку по физике С1 (25) Камень бросили вертикально вверх с начальной скоростью 15 м/с. Через какое минимальное время после броска потенциальная энергия камня отсчитанная от уровня точки бросания, будет в 8 раз больше кинетической энергии камня? Сопротивление воздуха пренебрежимо мало

Answer 1

Е=Е₁+Е₂   Е₁=mv²/2 -² кинетическая    Е₂=mgh - потенциальная; (3)
В верхней точке полная энергия   Е=mgH, где Н=V₀²/(2g);
 Е=mgV₀²/(2g); (1)
В точке , где Е₂ =8 Е₁  Е=Е₁+8 Е₁  Е=9Е₁; (2)
(1)=(2)  mgV₀²/(2g)=9Е₁   Е₁= mgV₀²/(18g)=mV₀²/(18)
Е₂=8*mV₀²/18= (4/9)mV₀²; (4)
(3)=(4)  
mgh=(4/9)mV₀²
h=(4/9)V₀²/g
h=4/9*225(м/с)²/(9,8м/с²)≈10м
h=V₀t-gt²/2
gt²/2-V₀t+h=0 решаем квадратное ур-е
5t²-15t+10=0
t²-3t+2=0
t=3+(-)√(9-2))
t₁=3-2,6=0,4(c)
t₂=5,6(c)
Ответ: мин время 0,4с энергия камня отсчитанная от уровня точки бросания, будет в 8 раз больше кинетической энергии камня 

Answer 2

Problem Analysis

We are given the initial velocity of a stone thrown vertically upwards, and we need to find the minimum time after the throw when the potential energy of the stone, measured from the level of the throwing point, will be 8 times greater than the kinetic energy of the stone. We can solve this problem by using the equations of kinetic and potential energy.

Solution

Let's denote the initial velocity of the stone as v0 and the time after the throw as t. We can use the following equations:

1. The potential energy of the stone at a certain height h is given by: PE = mgh, where m is the mass of the stone, g is the acceleration due to gravity, and h is the height.

2. The kinetic energy of the stone is given by: KE = (1/2)mv^2, where m is the mass of the stone and v is the velocity.

We are given that the potential energy of the stone, measured from the level of the throwing point, will be 8 times greater than the kinetic energy of the stone. Mathematically, this can be expressed as:

PE = 8 * KE

Substituting the equations for potential and kinetic energy, we get:

mgh = 8 * (1/2)mv^2

Simplifying the equation, we can cancel out the mass and rearrange the terms:

gh = 4v^2

Now, we can substitute the values given in the problem. The acceleration due to gravity, g, is approximately 9.8 m/s^2. The initial velocity, v0, is given as 15 m/s. We need to find the time, t, when the potential energy is 8 times greater than the kinetic energy.

Substituting the values into the equation, we get:

9.8h = 4(15)^2

Simplifying further:

9.8h = 900

Now, we can solve for h:

h = 900 / 9.8

Calculating the value:

h ≈ 91.84 meters

Therefore, the stone will have 8 times more potential energy than kinetic energy when it reaches a height of approximately 91.84 meters.

Answer

The minimum time after the throw when the potential energy of the stone, measured from the level of the throwing point, will be 8 times greater than the kinetic energy of the stone is when the stone reaches a height of approximately 91.84 meters.